# Homework Help: How many terms of the series are needed in order to estimate the exact sum within .01

1. Nov 6, 2011

### kuczmama

1. The problem statement, all variables and given/known data

How many terms of the series

Ʃ (-1)n/(ln(n+1))
n=1
are needed in order to estimate the exact sum within .01
2. Relevant equations

I know that I need to use the remainder estimate for the integral test where Rn=s-sn

and that ∫ from (n+1) to ∞ of f(x)dx $\leq$ Rn $\leq$ ∫ from (n) to ∞ of f(x)dx

3. The attempt at a solution

I tried to take the integral but I don't know how, and I cant figure out another way to approach the problem

2. Nov 6, 2011

### LCKurtz

Re: How many terms of the series are needed in order to estimate the exact sum within

I don't think you want to use an integral.

Hint: Don't you have a theorem for alternating series (with certain hypotheses) that compares the error to the first term not included?